# Communications of the ACM

Last byte

## Puzzled: Solutions and Sources

Last month (August 2009, p. 104) we posted a trio of brainteasers, including one as yet unsolved, concerning probability and intuition.

On the first puzzle, I can't seem to come up the probability of 0.5254.

Probability of one specific instance not happening - call this x
x = (1 - 1 / (38 ** 3)) =

Number of possible instances - call this y
y = 105 * 104 * 103 / (3 * 2)

Probability of none of the instances happening - call this z
z = x ** y

Probability of at least one instance happening (i.e probability of coming out ahead) - (1 - z)

1 - ((1 - (1 / (38 ** 3))) ** (105 * 104 * 103 / (3 * 2)))
You get 0.967167798

What did I do wrong? Or is this a calculator precision problem?

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